entropy Thermodynamics of Horizons from a Dual Quantum System Full Paper Entropy 2007, 9, ISSN c 2007 by MDPI
|
|
- Anastasia Jennings
- 5 years ago
- Views:
Transcription
1 Entropy 2007, 9, Full Paper entropy ISSN c 2007 by MDPI Thermodynamics of Horizons from a Dual Quantum System Sudipta Sarkar and T Padmanabhan IUCAA, Post Bag 4, Ganeshkhind, Pune , India sudipta@iucaa.ernet.in, paddy@iucaa.ernet.in Author to whom correspondence should be addressed. Received: 10 July 2007 / Accepted: 13 August 2007 / Published: 20 August 2007 Abstract: It was shown recently that, in the case of Schwarschild black hole, one can obtain the correct thermodynamic relations by studying a model quantum system and using a particular duality transformation. We study this approach further for the case a general spherically symmetric horizon. We show that the idea works for a general case only if we define the entropy S as a congruence ( observer ) dependent quantity and the energy E as the integral over the source of the gravitational acceleration for the congruence. In fact, in this case, one recovers the relation S = E/2T between entropy, energy and temperature previously proposed by one of us in gr-qc/ This approach also enables us to calculate the quantum corrections of the Bekenstein-Hawking entropy formula for all spherically symmetric horizons. Keywords: Thermodynamics; Dual Quantum System 1. Introduction There is an intriguing analogy between gravitational dynamics of horizons and thermodynamics (for a recent review, see ref. [1]). We do not have fundamental understanding of this though most people believe this indicates a deep and as yet undiscovered aspect of quantum gravity. The first results, of course, were that of black hole horizon [2], Rindler horizon [3] and De-Sitter horizon [4]. In the case of these (and other horizons) one can associate a temperature fairly unambiguously. In the case of blackhole horizon, one also associates an entropy. In the case of Rindler and De-Sitter horizon, the observer dependence of the horizon makes people uneasy as regard associating entropy to the horizon (and most people try not to take a clear stand on this matter!). On the other hand there are strong arguments suggesting all horizons have thermodynamic variables associated with them and entropy of
2 Entropy 2007, horizons is an observer dependent construct [5]. If so, one can associate thermodynamic laws with all horizons and in fact this appears to offer an entirely new perspective on gravity [6, 7]. In conventional systems, one can derive the laws of thermodynamics from a more fundamental theory statistical mechanics. In such systems, entropy can be defined as the logarithm of total number of accessible microstates corresponding to the same macrostate. The existence of an entropy associated with any horizon provides a strong motivation for one to look for certain microstates of the underlying quantum theory. Although there have been several attempts to derive black hole entropy formula from counting the possible microstates in both string and loop formalisms, a comprehensive understanding of this issue remain elusive. Given this state of affairs, there is justification to study various aspects of the horizon thermodynamics and try to construct phenomenological models based on them. Recently, Balazs et. al.[8] has proposed an intriguing model in which they have considered a dual thermodynamics corresponding to isolated Schwarzschild black hole and have tried to obtain the entropy from a dual theory, to which standard statistical mechanics is applicable. They show that the standard (black hole) thermodynamic relations are invariant under the transformations E A/4, S M, and T T 1 where A, M and T are the horizon area, mass and Hawking temperature of a black hole and E, S and T are the energy, entropy and temperature of the corresponding dual quantum system [8]. After working out the standard thermodynamics of the dual system, they apply the inverse transformations to get standard horizon thermodynamics as well as the logarithmic corrections to the original Bekenstein-Hawking entropy formula. This approach seem to provide a description of a strongly interacting gravitational system like black hole in terms of a weakly interacting quantum mechanical dual system. The result is sufficiently intriguing that one would like to understand its origin and domain of applicability. In particular one would like to know whether it generalizes for an arbitrary horizon (like e.g., De-Sitter horizon, which will play an important role in the study of cosmological constant [9]). We will address several aspects of this question in this paper in an attempt to understand this result. Any attempt to generalize these result beyond the Schwarzschild blackhole raises an operational issue: While one can define the temperature for a sufficiently general class of horizons (Schwarschild, Reissner- Nordstrom, De-Sitter, Rindler...), and even take entropy per unit transverse area to be (1/4) (so that non-compact horizons are also taken care of) it is not easy to define the energy associated with arbitrary horizons! Even for Reissner-Nordstrom blackhole there are different expressions for energy available in the literature (see e.g., [10, 11] and references cited therein). Fortunately, for all spherically symmetric metrics, there is a natural way of defining this quantity. This is explained in detail in ref.[6] and is essentially U = a/2 in geometric units where a is the horizon radius. However, we shall show below that, with this definition, one can not generalize the idea of duality to spherically symmetric spacetime in a consistent manner. On the other hand, one can define another expression for energy E which is the source of gravitational acceleration using the Tolman-Komar integral (see [12, 19]). It was shown in ref.[12] that this expression for energy also arises naturally in the case of any static horizon and allows one to obtain an equation of state between entropy, temperature and energy in the form S = E/2T. Surprisingly, this result arises directly from the duality model! We shall now describe these results in detail and provide a brief
3 Entropy 2007, discussion. Consider a static, spherically symmetric horizon, in the spacetime described by a metric (in which we have adopted natural units, with = c = G = 1): ds 2 = f(r)dt 2 1 f(r) dr2 r 2 dω 2. (1) We assume that the function f(r) has a simple zero at r = a with finite f (a) so that the spacetime has a horizon at r = a. Periodicity in Eulerian time allows us to associate a temperature T = f (a)/4π with the horizon. (Even for spacetimes with multi-horizons this prescription is locally valid for each horizon surface [6, 13]). The Bekenstein-Hawking entropy is equal to the one quarter of the horizon area and therefore is given by, S = 1 4 (4πa2 ) = πa 2. (2) These correspondences have been worked out in detail in [6]; when f (a) < 0, like in the case of De- Sitter, one needs to make appropriate sign changes, which is also explained in [6]. For our purpose we will ignore these complications. The real ambiguity is in giving a proper prescription for the energy a well known problem in general relativity. For the Schwarzschild black hole it is obviously equal to the total mass M, but for De- Sitter spacetime or even in the apparently simpler (asymptotically flat) case of a charged black hole, the definition of energy is non-trivial. We will handle this difficulty by not assuming a-priori any prescription for energy E; instead we will find its generic form if the duality principle is valid. Now, the duality transformation considered by in ref.[8] is, S E, E S, T 1 T and µ T µ. (3) Where µ is the chemical potential. Such a transformation will preserve the form of the first law of thermodynamics for both the black hole and the dual system. If we assume its validity and map a general spherically symmetric horizon to its dual system, we get the expressions for energy, entropy and temperature for the dual system to be: S d = E, E d = πa 2, and T d = 4π f (a). (4) (Note that we are not assuming any specific form for the energy E of the horizon.) Taking the dual system as a one dimensional Bose gas, the expressions for energy and entropy are given by [8], E d = pl = 1 12 glπt d 2 gl 2π (log ( µ d/t d ) 1) T d µ d gl 8π µ2 d + O ( ) µ 3 d, (5) S d = 1 6 glπt d gl 2π (log( µ d/t d ) 1)µ d + O ( ) µ 3 d. (6) (One can easily perform all the calculations for the Fermi gas.) The coefficient g is the internal degrees of freedom of the gas particles and L is the size of the system. Consistency requires that the leading order term of the entropy of the dual system gives correct value of of the black hole energy under the reverse transformation. This fixes the value of the quantity gl is uniquely as gl = 3Ef (a)/2π 2, With this value of gl, the leading term in the expression of energy E d of the dual system becomes, E d = 2πE f (a). (7)
4 Entropy 2007, If under a reverse transformation this expression gives the correct black hole entropy, one must have, πa 2 = 2Eπ/f (a) thereby allowing us to determine the energy associated with the horizon E = a2 f (a). (8) 2 The above analysis is exactly the same as the one performed in ref.[8] but for general context, keeping E unspecified but S = πa 2, T = f (a)/4π. We stress that we have not done anything drastic or unconventional except to adhere to the duality prescription. For Schwarzschild spacetime a = 2M, and f (a) = 1/2M and the above equation will give correct value of energy E = M if we have af (a) = 1. This condition is trivially satisfied for Schwarzschild blackhole. This is essentially the result of [8]. Let us next try Reissner-Nordstrom blackhole. Then f(r) = (1 2M/r + Q 2 /r 2 ) and the horizon is at a = M + M 2 Q 2. The temperature associated with this outer horizon is T = κ/2π where κ is the surface gravity of the outer horizon. In this case it is easy to see that af (a) = 2M/a 2Q 2 /a 2 (so that af (a) 1 unless Q = 0). If we require this analysis to be applicable for charged black holes also, the energy E should be given by Eq. (8): E = a2 f (a) = M Q2 2 a = M 2 Q 2. (9) In the literature several expressions are given for energy of Reissner-Nordstrom metric and this one corresponds to Moller energy for Reissner-Nordstrom black hole [10, 11]. However, since our motivation is to study the thermodynamics of the horizons, any definition of energy should come from a thermodynamic consideration. But the expression of the energy in Eq. (9) does not agree with this prescription. For example, if we drop an uncharged particle of mass M into a Reissner-Nordstrom blackhole, its energy should change by dm and the resulting change in entropy should be related to this by de = T ds. But if we start with the expression of energy in Eq. (9), then the change in mass will result in a change in energy de = MdM/ M 2 Q 2. On the other hand T ds = (M/a Q 2 /a 2 ) da = dm which does not match de. Therefore the energy expression in Eq. (9) does not have a proper thermodynamic interpretation. There is, however, another interesting interpretation possible for this result, which is based on the formalism developed in ref.[12]. We shall briefly recall this result, which is based on the point of view that the entropy associated with any horizon is due to the information which are hidden by the horizon. In order to formulate this idea mathematically, we need to set up the geometrical framework which is adapted to a congruence of observers who sees a horizon. The metric of a static spacetime can always be put in the form ds 2 = N 2 dt 2 + γ µν dx µ dx ν, where N and γ µν are independent of time t (Greek indices cover 1,2,3 and Latin indices cover 0-3). The comoving observer at x µ =constant have the four velocity u i = Nδi 0 and the four acceleration a i = (0, µ N/N). If N 0 on a two-surface and Na = (γ µν µ N ν N) 1/2 is finite (say κ, the surface gravity), then the coordinate system has a horizon. Regularity in the Euclidean sector requires the periodicity in Euclidean time with the period β = 2π/κ, allowing us to define a temperature T = β 1 in terms of the derivatives of N, whenever there is a horizon. The expression for entropy associated with this horizon is given as [12], S = 1 8πG g d 4 x i a i. (10)
5 Entropy 2007, Obviously, the entropy defined by the above expression depends on the choice of the congruence, through the four vector u i, but is generally covariant. (For justification behind this definition of gravitational entropy, see ref.[12]). Now, in any spacetime, there is a differential geometric identity [14], R bd u b u d = i (Ku i + a i ) K ab K ab + K a ak b b. (11) where K ab is the extrinsic curvature of spatial hypersurfaces and K is its trace. In static spacetime we have K ab = 0 and when combined with Einstein s equation we can write: 1 8πG ia i = (T ab 1 2 T g ab)u a u b. (12) This equation relates the integrand of Eq. (10) to the matter stress tensor T ab. We next note that the source for gravitational acceleration is the covariant combination (T ab 1T g 2 ab)u a u b, and the corresponding energy E is given by Tolman-Komar integral [19], E = 2 d 3 x γn(t ab 1 2 T g ab)u a u b. (13) From Eq. (10), Eq. (8) and Eq. (12), we can easily find that, V S = 1 βe. (14) 2 A closer inspection of the Eq. (8) and Eq. (2) reveals that there exits a exactly the same relationship between entropy S and energy E defined by the dual system approach! All these results can be easily extended to a general D dimension by noting the fact even in D dimension the entropy is still one quarter of the area of the black hole horizon and therefore for a D dimensional spherically symmetric spacetime, the entropy of the horizon is given by, S (D) = A D 2a D 2, (15) 4 where A D 2 is the area of a (D 2) dimensional unit sphere. The temperature of the horizon is still T = f (a)/4π and let the relevant energy is E (D). Then the dual transformations are, S (D) E (D), E (D) S, T 1 T and µ T µ. (16) Therefore for the dual system we have: S d = E (D), E d = A D 2a D 2, and T d = 4π 4 f (a). (17) Taking the dual system as a one dimensional Bose gas, and using the expressions for energy and entropy in Eq. (6), it is straightforward to determine the energy associated with the horizon as, E (D) = A D 2a D 2 f (a). (18) 8π This reduces to Eq. (8) for the case of D = 4. On the other hand, for the case of general D dimension the entropy definition in Eq. (10) should be modified as, S = 1 g d D x i a i. (19) 8π
6 Entropy 2007, The differential identity in Eq. (11) is valid in any dimension. Therefore we will have in D dimensions, 1 8π ia i = (T ab 1 D 2 T g ab)u a u b. (20) The Komar integral in D dimension is, E = 1 8π lim α ξ β s t (t) ds αβ (21) s t where ds αβ is the surface element in (D 2) dimensional hypersurface and ξ β (t) is the spacetime s timelike killing vector. We also have Stokes theorem for antisymmetric tensor field B αβ given by [14] 1 B αβ ds αβ = B αβ ;β 2 dv α (22) In our case B αβ = α ξ β (t). Then using killing equation we can write, V V B αβ ;β = ( α ξ β ) ;β = ξ α (23) Now all killing vectors satisfies the identity ξ α = Rβ αξβ. Using this identity along with Einstein equations, it is straightforward to prove that, E = 2 d D 1 x γn(t ab 1 D 2 T g ab)u a u b. (24) V Therefore, 2 factor in the front is universal and does not depend on the dimensions. Hence from Eq. (12) and Eq. (24) we can easily show that the original relationship S = βe/2 prevails in case of general D dimensions also. Therefore, the natural conclusion of our analysis is that, the generalization of this duality transformations in [8] for any spherically symmetric horizon is only possible when the entropy and the energy associated with the horizon are defined in accordance with ref.[12]. That is, the energy-entropy duality in general should be taken as a dual transformation between the entropy S in Eq. (10) and energy E in Eq. (13), so that the relationship Eq. (14) will always be satisfied. This will ensure the consistency of the entire approach and give the correct value of the Bekenstein-Hawking entropy under reverse transformation. For the sake of completeness we also calculate quantum corrections to the horizon entropy for a general spherically symmetric horizon, using corrections to the energy of the dual quantum gas. The energy of the Bose model is E d = pl = 1 12 glπt d 2 gl 2π (log ( µ d/t d ) 1) T d µ d gl 8π µ2 d + O ( ) µ 3 d. (25) Using gl = 3Ef (a)/2π 2, and performing the reverse transformation, the entropy of the horizon is obtained as, S = πa 2 + 6a2 π (log µ 1) µ 3a2 2π µ2 + O ( µ 3). (26)
7 Entropy 2007, Quantum corrections to the entropy of various black holes were determined using the Cardy formula [15, 17, 18]. In order to obtain the correct coefficient of the logarithmic quantum correction term [16] we need to fix the value of µ as, With this choice of µ the entropy of the horizon becomes, S = πa log (πa2 ) 3 2 µ = π 4a 2 (27) ( 1 + log ( )) (28) π 2 For Schwarzschild case a = 2M, and we recover the correct expression for the black hole entropy with logarithmic quantum corrections as shown in [8]. The actual value is, of course, obtained by adjusting the free parameter µ in the theory and hence is not so important; but the fact that the nature of the corrections have the logarithmic form is interesting and is worthy of futher investigation. If the duality ideas are correct, these terms are also universal and is applicable to all horizons. 2. Conclusion Our analysis clearly shows that it is indeed possible to generalize the duality principle in [8] for a generic spherically symmetric horizon provided the definition of entropy and energy are in accordance with the results obtained in ref. [12]. This suggests that the approach of understanding the horizon thermodynamics based of a duality transformation is possibly quite generic and therefore may be important for the understanding of the underlying quantum theory. Acknowledgements One of the author (S.S.) is supported by the Council of Scientific & Industrial Research, India. References 1. (a) Padmanabhan, T. Gravity and the Thermodynamics of Horizon. Phys. Rept. 2005, 406, ; (b) Padmanabhan, T. Thermodynamics and/of Horizons: A Comparison of Schwarzschild, RINDLER and desitter Spacetimes. Mod. Phys. Letts. 2002, A 17, 923 [gr-qc/ ]. 2. Hawkings, S.W. Particle creation by black holes. Commun. Math. Phys. 1975, 43, (a) Davies, P.C.W. Scalar particle production in Schwarzschild and Rindler metrics. J. Phys. A 1975, 8, ; (b) Unruh, W.G. Notes on Black hole Evaporation. Phys. Rev. D 1976, 14, Gibbons, G.; Hawking, S. Cosmological event horizons, thermodynamics, and particle creation. Phys. Rev. D 1977, 15, (a) Jacobson, T.; Parentani, R. Horizon Entropy. Found. Phys. 2003, 33, [gr-qc/ ]; (b) Culetu, H. Is the Rindler horizon energy nonvanishing? [hep-th/ ]; (c) Padmanabhan, T. Is gravity an intrinsically quantum phenomenon? Dynamics of Gravity from the Entropy of Spacetime and the Principle of Equivalence. Mod. Phys. Letts. A 2002, 17, 1147 [hep-th/ ]; (d) Padmanabhan, T. Topological interpretation of the horizon temperature. Mod. Phys. Letts. A
8 Entropy 2007, , 2903 [hep-th/ ]; (e) Padmanabhan, T. The Holography of gravity encoded in a relation between Entropy, Horizon Area and the Action for gravity. Gen. Rel. Grav 2002, 34, [gr-qc/ ]; (f) Padmanabhan, T. Gravity from Spacetime Thermodynamics. Ap. Sp. Sc. 2003, 285, 407 [gr-qc/ ]; (g) Padmanabhan, T. Why gravity has no choice: Bulk spacetime dynamics is dictated by information entanglement across horizons. Gen. Rel. Grav. 2003, 35, Padmanabhan, T. Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes. Class. Quan. Grav. 2002, 19, 5387 [gr-qc/ ]. 7. (a) Padmanabhan, T. A new perspective on Gravity and the dynamics of Spacetime. Int. J. Mod. Phys. 2005, D14, [gr-qc/ ]; (b) Padmanabhan, T. Gravity: A New Holographic Perspective. Braz. Jour. Phys. 2005, 35(Special Issue), 362 [gr-qc/ ], [gr-qc/ ]; (c) Jacobson, T. Thermodynamics of Spacetime: The Einstein Equation of State. Phys. Rev. Lett. 1995, 75, [gr-qc/ ]. 8. Balazs, C.; Szapudi, I. Holographic Quantum Statistics from Dual Thermodynamics [hep-th/ ]. 9. Padmanabhan, T. Cosmological Constant - the Weight of the Vacuum. Phys. Rep. 2003, 380, [hep-th/ ]. 10. Salti, M.; Aydogdu, O. Energy Distribution in Reissner-Nordstrom anti-de Sitter black holes in Moller Prescription [gr-qc/ ]. 11. Vagenas, E.C. Energy distribution in the dyadosphere of a Reissner-Nordstrom black hole in Moller s prescription [gr-qc/ ]. 12. Padmanabhan, T. Entropy of Static Spacetimes and Microscopic Density of States. Class. Quant. Grav. 2004, 21, [gr-qc/ ]. 13. Choudhury, T.R.; Padmanabhan, T. Quasi normal modes in Schwarzschild-DeSitter spacetime: A simple derivation of the level spacing of the frequencies [gr-qc/ ]. 14. Misner, C.; Thorne, K.; Wheeler, J. Gravitation, Freeman and Co., (a) Cardy, J.L. Operator content of two-dimensional conformally invariant theories. Nucl. Phys. 1986, B270, ; (b) Bloete, H.W.J.; Cardy, J.L.; Nightingale, M.P. Conformal invariance, the central charge, and universal finite-size amplitudes at criticality. Phys. Rev. Lett. 1986, 56, Kaul, R.K.; Majumdar, P. Logarithmic correction to the Bekenstein-Hawking entropy. Phys. Rev. Lett. 2000, 84, [gr-qc/ ]. 17. Das, S.; Kaul, R.K.; Majumdar, P. A new holographic entropy bound from quantum geometry. Phys. Rev. 2001, D63, [hep-th/ ]. 18. Park, M.-I. Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy. JHEP, 2004, 0412, 041 [hep-th/ ]. 19. (a) Tolman, R.C. On the Use of the Energy-Momentum Principle in General Relativity. Phys. Rev. 1930, 35, 875; (b) Komar, A. Covariant Conservation Laws in General Relativity. Phys. Rev. 1959, 113, 934. c 2007 by MDPI ( Reproduction is permitted for noncommercial purposes.
On the Hawking Wormhole Horizon Entropy
ESI The Erwin Schrödinger International Boltzmanngasse 9 Institute for Mathematical Physics A-1090 Wien, Austria On the Hawking Wormhole Horizon Entropy Hristu Culetu Vienna, Preprint ESI 1760 (2005) December
More informationHolography for 3D Einstein gravity. with a conformal scalar field
Holography for 3D Einstein gravity with a conformal scalar field Farhang Loran Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran. Abstract: We review AdS 3 /CFT 2 correspondence
More informationA Comment on Curvature Effects In CFTs And The Cardy-Verlinde Formula
A Comment on Curvature Effects In CFTs And The Cardy-Verlinde Formula Arshad Momen and Tapobrata Sarkar the Abdus Salam International Center for Theoretical Physics, Strada Costiera, 11 4014 Trieste, Italy
More informationκ = f (r 0 ) k µ µ k ν = κk ν (5)
1. Horizon regularity and surface gravity Consider a static, spherically symmetric metric of the form where f(r) vanishes at r = r 0 linearly, and g(r 0 ) 0. Show that near r = r 0 the metric is approximately
More informationarxiv: v2 [gr-qc] 27 Apr 2013
Free of centrifugal acceleration spacetime - Geodesics arxiv:1303.7376v2 [gr-qc] 27 Apr 2013 Hristu Culetu Ovidius University, Dept.of Physics and Electronics, B-dul Mamaia 124, 900527 Constanta, Romania
More informationarxiv: v1 [hep-th] 3 Feb 2016
Noname manuscript No. (will be inserted by the editor) Thermodynamics of Asymptotically Flat Black Holes in Lovelock Background N. Abbasvandi M. J. Soleimani Shahidan Radiman W.A.T. Wan Abdullah G. Gopir
More informationarxiv:hep-th/ v2 15 Jan 2004
hep-th/0311240 A Note on Thermodynamics of Black Holes in Lovelock Gravity arxiv:hep-th/0311240v2 15 Jan 2004 Rong-Gen Cai Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735,
More informationSynchronization of thermal Clocks and entropic Corrections of Gravity
Synchronization of thermal Clocks and entropic Corrections of Gravity Andreas Schlatter Burghaldeweg 2F, 5024 Küttigen, Switzerland schlatter.a@bluewin.ch Abstract There are so called MOND corrections
More informationarxiv: v1 [gr-qc] 10 Nov 2018
Thermal fluctuations to thermodynamics of non-rotating BTZ black hole Nadeem-ul-islam a, Prince A. Ganai a, and Sudhaker Upadhyay c,d a Department of Physics, National Institute of Technology, Srinagar,
More informationThe Role of Black Holes in the AdS/CFT Correspondence
The Role of Black Holes in the AdS/CFT Correspondence Mario Flory 23.07.2013 Mario Flory BHs in AdS/CFT 1 / 30 GR and BHs Part I: General Relativity and Black Holes Einstein Field Equations Lightcones
More informationDoes the third law of black hole thermodynamics really have a serious failure?
Does the third law of black hole thermodynamics really have a serious failure? István Rácz KFKI Research Institute for Particle and Nuclear Physics H-1525 Budapest 114 P.O.B. 49, Hungary September 16,
More informationIs gravity an intrinsically quantum phenomenon? Dynamics of Gravity from the Entropy of Spacetime and the Principle of Equivalence
Modern Physics Letters A, c World Scientific Publishing Company Is gravity an intrinsically quantum phenomenon? Dynamics of Gravity from the Entropy of Spacetime and the Principle of Equivalence T. PADMANABHAN
More informationGauss-Bonnet Black Holes in ds Spaces. Abstract
USTC-ICTS-03-5 Gauss-Bonnet Black Holes in ds Spaces Rong-Gen Cai Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 735, Beijing 00080, China Interdisciplinary Center for Theoretical
More informationarxiv: v2 [gr-qc] 22 Jan 2014
Regular black hole metrics and the weak energy condition Leonardo Balart 1,2 and Elias C. Vagenas 3 1 I.C.B. - Institut Carnot de Bourgogne UMR 5209 CNRS, Faculté des Sciences Mirande, Université de Bourgogne,
More informationHolography on the Horizon and at Infinity
Holography on the Horizon and at Infinity Suvankar Dutta H. R. I. Allahabad Indian String Meeting, PURI 2006 Reference: Phys.Rev.D74:044007,2006. (with Rajesh Gopakumar) Work in progress (with D. Astefanesei
More informationarxiv:hep-th/ v1 7 Apr 2003
UB-ECM-PF-03/10 Cardy-Verlinde Formula and Achúcarro-Ortiz Black Hole Mohammad R. Setare 1 and Elias C. Vagenas arxiv:hep-th/0304060v1 7 Apr 003 1 Department of Physics, Sharif University of Technology,
More informationGRAVITY: THE INSIDE STORY
GRAVITY: THE INSIDE STORY T. Padmanabhan (IUCAA, Pune, India) VR Lecture, IAGRG Meeting Kolkatta, 28 Jan 09 CONVENTIONAL VIEW GRAVITY AS A FUNDAMENTAL INTERACTION CONVENTIONAL VIEW GRAVITY AS A FUNDAMENTAL
More informationTHE HYDRODYNAMICS OF ATOMS OF SPACETIME: GRAVITATIONAL FIELD EQUATION IS NAVIER STOKES EQUATION
International Journal of Modern Physics D Vol. 20, No. 14 (2011) 2817 2822 c World Scientific Publishing Company DOI: 10.1142/S0218271811020603 THE HYDRODYNAMICS OF ATOMS OF SPACETIME: GRAVITATIONAL FIELD
More informationarxiv:gr-qc/ v1 24 Sep 2002
Gravity from Spacetime Thermodynamics T. Padmanabhan IUCAA, Pune University Campus, Pune 411 007 (nabhan@iucaa.ernet.in) arxiv:gr-qc/0209088v1 24 Sep 2002 Abstract. The Einstein-Hilbert action (and thus
More informationBOUNDARY STRESS TENSORS IN A TIME DEPENDENT SPACETIME
BOUNDARY STRESS TENSORS IN A TIME DEPENDENT SPACETIME Hristu Culetu, Ovidius University, Dept.of Physics, B-dul Mamaia 124, 8700 Constanta, Romania, e-mail : hculetu@yahoo.com October 12, 2007 Abstract
More informationDo semiclassical zero temperature black holes exist?
Do semiclassical zero temperature black holes exist? Paul R. Anderson Department of Physics, Wake Forest University, Winston-Salem, North Carolina 7109 William A. Hiscock, Brett E. Taylor Department of
More informationStudying the cosmological apparent horizon with quasistatic coordinates
PRAMANA c Indian Academy of Sciences Vol. 80, No. journal of February 013 physics pp. 349 354 Studying the cosmological apparent horizon with quasistatic coordinates RUI-YAN YU 1, and TOWE WANG 1 School
More informationA rotating charged black hole solution in f (R) gravity
PRAMANA c Indian Academy of Sciences Vol. 78, No. 5 journal of May 01 physics pp. 697 703 A rotating charged black hole solution in f R) gravity ALEXIS LARRAÑAGA National Astronomical Observatory, National
More informationThermodynamics of hot quantum scalar field in a (D + 1) dimensional curved spacetime
EJTP 4, No. 37 (08) 5 4 Electronic Journal of Theoretical Physics Thermodynamics of hot quantum scalar field in a (D + ) dimensional curved spacetime W. A. Rojas C. and J. R. Arenas S. Received 6 August
More informationBlack holes, Holography and Thermodynamics of Gauge Theories
Black holes, Holography and Thermodynamics of Gauge Theories N. Tetradis University of Athens Duality between a five-dimensional AdS-Schwarzschild geometry and a four-dimensional thermalized, strongly
More informationSymmetries, Horizons, and Black Hole Entropy. Steve Carlip U.C. Davis
Symmetries, Horizons, and Black Hole Entropy Steve Carlip U.C. Davis UC Davis June 2007 Black holes behave as thermodynamic objects T = κ 2πc S BH = A 4 G Quantum ( ) and gravitational (G) Does this thermodynamic
More informationIntroductory Course on Black Hole Physics and AdS/CFT Duality Lecturer: M.M. Sheikh-Jabbari
Introductory Course on Black Hole Physics and AdS/CFT Duality Lecturer: M.M. Sheikh-Jabbari This is a PhD level course, designed for second year PhD students in Theoretical High Energy Physics (HEP-TH)
More informationThe Apparent Universe
The Apparent Universe Alexis HELOU APC - AstroParticule et Cosmologie, Paris, France alexis.helou@apc.univ-paris7.fr 11 th June 2014 Reference This presentation is based on a work by P. Binétruy & A. Helou:
More informationClassical Oscilators in General Relativity
Classical Oscilators in General Relativity arxiv:gr-qc/9709020v2 22 Oct 2000 Ion I. Cotăescu and Dumitru N. Vulcanov The West University of Timişoara, V. Pârvan Ave. 4, RO-1900 Timişoara, Romania Abstract
More informationIntroduction to AdS/CFT
Introduction to AdS/CFT Who? From? Where? When? Nina Miekley University of Würzburg Young Scientists Workshop 2017 July 17, 2017 (Figure by Stan Brodsky) Intuitive motivation What is meant by holography?
More informationarxiv:gr-qc/ v1 2 Mar 1999
Universal Upper Bound to the Entropy of a Charged System Shahar Hod The Racah Institute for Physics, The Hebrew University, Jerusalem 91904, Israel (June 6, 2018) arxiv:gr-qc/9903010v1 2 Mar 1999 Abstract
More informationarxiv:gr-qc/ v2 1 Oct 1998
Action and entropy of black holes in spacetimes with cosmological constant Rong-Gen Cai Center for Theoretical Physics, Seoul National University, Seoul, 151-742, Korea Jeong-Young Ji and Kwang-Sup Soh
More informationarxiv:gr-qc/ v2 11 Feb 2003
Gravity from Spacetime Thermodynamics T. Padmanabhan IUCAA, Pune University Campus, Pune 411 007 (nabhan@iucaa.ernet.in) arxiv:gr-qc/0209088v2 11 Feb 2003 Abstract. The Einstein-Hilbert action (and thus
More informationTheoretical Aspects of Black Hole Physics
Les Chercheurs Luxembourgeois à l Etranger, Luxembourg-Ville, October 24, 2011 Hawking & Ellis Theoretical Aspects of Black Hole Physics Glenn Barnich Physique théorique et mathématique Université Libre
More informationHolography Duality (8.821/8.871) Fall 2014 Assignment 2
Holography Duality (8.821/8.871) Fall 2014 Assignment 2 Sept. 27, 2014 Due Thursday, Oct. 9, 2014 Please remember to put your name at the top of your paper. Note: The four laws of black hole mechanics
More informationThe Cardy-Verlinde equation and the gravitational collapse. Cosimo Stornaiolo INFN -- Napoli
The Cardy-Verlinde equation and the gravitational collapse Cosimo Stornaiolo INFN -- Napoli G. Maiella and C. Stornaiolo The Cardy-Verlinde equation and the gravitational collapse Int.J.Mod.Phys. A25 (2010)
More informationHawking radiation and universal horizons
LPT Orsay, France June 23, 2015 Florent Michel and Renaud Parentani. Black hole radiation in the presence of a universal horizon. In: Phys. Rev. D 91 (12 2015), p. 124049 Hawking radiation in Lorentz-invariant
More informationNear horizon geometry, Brick wall model and the Entropy of a scalar field in the Reissner-Nordstrom black hole backgrounds
Near horizon geometry, Brick wall model and the Entropy of a scalar field in the Reissner-Nordstrom black hole backgrounds Kaushik Ghosh 1 Department of Physics, St. Xavier s College, 30, Mother Teresa
More informationThermodynamics of spacetime in generally covariant theories of gravitation
Thermodynamics of spacetime in generally covariant theories of gravitation Christopher Eling Department of Physics, University of Maryland, College Park, MD 20742-4111, USA draft of a paper for publication
More informationExpanding plasmas from Anti de Sitter black holes
Expanding plasmas from Anti de Sitter black holes (based on 1609.07116 [hep-th]) Giancarlo Camilo University of São Paulo Giancarlo Camilo (IFUSP) Expanding plasmas from AdS black holes 1 / 15 Objective
More informationarxiv:gr-qc/ v1 26 Aug 1997
Action and entropy of lukewarm black holes SNUTP 97-119 Rong-Gen Cai Center for Theoretical Physics, Seoul National University, Seoul, 151-742, Korea arxiv:gr-qc/9708062v1 26 Aug 1997 Jeong-Young Ji and
More information31st Jerusalem Winter School in Theoretical Physics: Problem Set 2
31st Jerusalem Winter School in Theoretical Physics: Problem Set Contents Frank Verstraete: Quantum Information and Quantum Matter : 3 : Solution to Problem 9 7 Daniel Harlow: Black Holes and Quantum Information
More informationarxiv:hep-th/ v1 31 Jan 2006
hep-th/61228 arxiv:hep-th/61228v1 31 Jan 26 BTZ Black Hole with Chern-Simons and Higher Derivative Terms Bindusar Sahoo and Ashoke Sen Harish-Chandra Research Institute Chhatnag Road, Jhusi, Allahabad
More informationATOMS OF SPACETIME. Fourth Abdus Salaam Memorial Lecture ( ) T. Padmanabhan (IUCAA, Pune, India) Feb. 28, 2006
ATOMS OF SPACETIME T. Padmanabhan (IUCAA, Pune, India) Feb. 28, 2006 Fourth Abdus Salaam Memorial Lecture (2005-2006) WHAT WILL BE THE VIEW REGARDING GRAVITY AND SPACETIME IN THE YEAR 2206? CLASSICAL GRAVITY
More informationA. Larrañaga 1,2 1 Universidad Nacional de Colombia. Observatorio Astronomico Nacional. 1 Introduction
Bulg. J. Phys. 37 (2010) 10 15 Thermodynamics of the (2 + 1)-dimensional Black Hole with non linear Electrodynamics and without Cosmological Constant from the Generalized Uncertainty Principle A. Larrañaga
More informationA UNIFIED TREATMENT OF GRAVITATIONAL COLLAPSE IN GENERAL RELATIVITY
A UNIFIED TREATMENT OF GRAVITATIONAL COLLAPSE IN GENERAL RELATIVITY & Anthony Lun Fourth Aegean Summer School on Black Holes Mytilene, Island of Lesvos 17/9/2007 CONTENTS Junction Conditions Standard approach
More informationarxiv:hep-th/ v3 25 Sep 2006
OCU-PHYS 46 AP-GR 33 Kaluza-Klein Multi-Black Holes in Five-Dimensional arxiv:hep-th/0605030v3 5 Sep 006 Einstein-Maxwell Theory Hideki Ishihara, Masashi Kimura, Ken Matsuno, and Shinya Tomizawa Department
More informationDeformations of Spacetime Horizons and Entropy
Adv. Studies Theor. Phys., ol. 7, 2013, no. 22, 1095-1100 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/astp.2013.39100 Deformations of Spacetime Horizons and Entropy Paul Bracken Department
More informationEMERGENT GRAVITY AND COSMOLOGY: THERMODYNAMIC PERSPECTIVE
EMERGENT GRAVITY AND COSMOLOGY: THERMODYNAMIC PERSPECTIVE Master Colloquium Pranjal Dhole University of Bonn Supervisors: Prof. Dr. Claus Kiefer Prof. Dr. Pavel Kroupa May 22, 2015 Work done at: Institute
More informationBlack Hole Entropy and Gauge/Gravity Duality
Tatsuma Nishioka (Kyoto,IPMU) based on PRD 77:064005,2008 with T. Azeyanagi and T. Takayanagi JHEP 0904:019,2009 with T. Hartman, K. Murata and A. Strominger JHEP 0905:077,2009 with G. Compere and K. Murata
More informationEntanglement and the Bekenstein-Hawking entropy
Entanglement and the Bekenstein-Hawking entropy Eugenio Bianchi relativity.phys.lsu.edu/ilqgs International Loop Quantum Gravity Seminar Black hole entropy Bekenstein-Hawking 1974 Process: matter falling
More informationEntropy of Quasiblack holes and entropy of black holes in membrane approach
Entropy of Quasiblack holes and entropy of black holes in membrane approach José P. S. Lemos Centro Multidisciplinar de Astrofísica, CENTRA, Lisbon, Portugal Oleg B. Zaslavskii Department of Physics and
More informationThe Einstein-Hilbert Action, Horizons and Connections with Thermodynamics
Adv. Studies Theor. Phys., ol. 6, 2012, no. 2, 83-93 The Einstein-Hilbert Action, Horizons and Connections with Thermodynamics Paul Bracken Department of Mathematics University of Texas, Edinburg TX 78541-2999,
More informationQuantum Entanglement and the Geometry of Spacetime
Quantum Entanglement and the Geometry of Spacetime Matthew Headrick Brandeis University UMass-Boston Physics Colloquium October 26, 2017 It from Qubit Simons Foundation Entropy and area Bekenstein-Hawking
More informationI wish to further comment on these issues. Not much technical details; just to raise awareness
Yen Chin Ong Unruh: Can information fall off the edge of spacetime (singularity)? No evidence except prejudice that this is not the case AdS/CFT: Can boundary probe BH interior? Bag-of-gold? ER-bridge?
More informationThin shell wormholes in higher dimensiaonal Einstein-Maxwell theory
Thin shell wormholes in higher dimensiaonal Einstein-Maxwell theory arxiv:gr-qc/6761v1 17 Jul 6 F.Rahaman, M.Kalam and S.Chakraborty Abstract We construct thin shell Lorentzian wormholes in higher dimensional
More informationBlack Hole Entropy: An ADM Approach Steve Carlip U.C. Davis
Black Hole Entropy: An ADM Approach Steve Carlip U.C. Davis ADM-50 College Station, Texas November 2009 Black holes behave as thermodynamic objects T = κ 2πc S BH = A 4 G Quantum ( ) and gravitational
More informationBlack hole thermodynamics
Black hole thermodynamics Daniel Grumiller Institute for Theoretical Physics Vienna University of Technology Spring workshop/kosmologietag, Bielefeld, May 2014 with R. McNees and J. Salzer: 1402.5127 Main
More informationarxiv: v1 [gr-qc] 2 Sep 2015
Entropy Product Formula for spinning BTZ Black Hole Parthapratim Pradhan 1 arxiv:1509.0066v1 [gr-qc] Sep 015 Department of Physics Vivekananda Satavarshiki Mahavidyalaya (Affiliated to Vidyasagar University)
More informationA Brief Introduction to AdS/CFT Correspondence
Department of Physics Universidad de los Andes Bogota, Colombia 2011 Outline of the Talk Outline of the Talk Introduction Outline of the Talk Introduction Motivation Outline of the Talk Introduction Motivation
More informationEXTREMELY CHARGED STATIC DUST DISTRIBUTIONS IN GENERAL RELATIVITY
arxiv:gr-qc/9806038v1 8 Jun 1998 EXTREMELY CHARGED STATIC DUST DISTRIBUTIONS IN GENERAL RELATIVITY METÍN GÜRSES Mathematics department, Bilkent University, 06533 Ankara-TURKEY E-mail: gurses@fen.bilkent.edu.tr
More informationElectromagnetic Energy for a Charged Kerr Black Hole. in a Uniform Magnetic Field. Abstract
Electromagnetic Energy for a Charged Kerr Black Hole in a Uniform Magnetic Field Li-Xin Li Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (December 12, 1999) arxiv:astro-ph/0001494v1
More informationarxiv: v1 [gr-qc] 1 Aug 2016
Stability Aspects of Wormholes in R Gravity James B. Dent a, Damien A. Easson b, Thomas W. Kephart c, and Sara C. White a a Department of Physics, University of Louisiana at Lafayette, Lafayette, LA 70504,
More informationWHY BLACK HOLES PHYSICS?
WHY BLACK HOLES PHYSICS? Nicolò Petri 13/10/2015 Nicolò Petri 13/10/2015 1 / 13 General motivations I Find a microscopic description of gravity, compatibile with the Standard Model (SM) and whose low-energy
More informationOn the Origin of Gravity and the Laws of Newton
S.N.Bose National Centre for Basic Sciences,India S.N. Bose National Centre for Basic Sciences, India Dept. of Theoretical Sciences 1 st April, 2010. E. Verlinde, arxiv:1001.0785 PLAN OF THE TALK (i) Why
More information21 July 2011, USTC-ICTS. Chiang-Mei Chen 陳江梅 Department of Physics, National Central University
21 July 2011, Seminar @ USTC-ICTS Chiang-Mei Chen 陳江梅 Department of Physics, National Central University Outline Black Hole Holographic Principle Kerr/CFT Correspondence Reissner-Nordstrom /CFT Correspondence
More informationThe Horizon Energy of a Black Hole
arxiv:1712.08462v1 [gr-qc] 19 Dec 2017 The Horizon Energy of a Black Hole Yuan K. Ha Department of Physics, Temple University Philadelphia, Pennsylvania 19122 U.S.A. yuanha@temple.edu December 1, 2017
More informationThe Holographic Principal and its Interplay with Cosmology. T. Nicholas Kypreos Final Presentation: General Relativity 09 December, 2008
The Holographic Principal and its Interplay with Cosmology T. Nicholas Kypreos Final Presentation: General Relativity 09 December, 2008 What is the temperature of a Black Hole? for simplicity, use the
More informationhas a lot of good notes on GR and links to other pages. General Relativity Philosophy of general relativity.
http://preposterousuniverse.com/grnotes/ has a lot of good notes on GR and links to other pages. General Relativity Philosophy of general relativity. As with any major theory in physics, GR has been framed
More informationarxiv:gr-qc/ v4 23 Feb 1999
gr-qc/9802042 Mod. Phys. Lett. A 3 (998) 49-425 Mass of perfect fluid black shells Konstantin G. Zloshchastiev arxiv:gr-qc/9802042v4 23 Feb 999 Department of Theoretical Physics, Dnepropetrovsk State University,
More informationQGP, Hydrodynamics and the AdS/CFT correspondence
QGP, Hydrodynamics and the AdS/CFT correspondence Adrián Soto Stony Brook University October 25th 2010 Adrián Soto (Stony Brook University) QGP, Hydrodynamics and AdS/CFT October 25th 2010 1 / 18 Outline
More informationGeometric inequalities for black holes
Geometric inequalities for black holes Sergio Dain FaMAF-Universidad Nacional de Córdoba, CONICET, Argentina. 3 August, 2012 Einstein equations (vacuum) The spacetime is a four dimensional manifold M with
More informationSPACETIME FROM ENTANGLEMENT - journal club notes -
SPACETIME FROM ENTANGLEMENT - journal club notes - Chris Heinrich 1 Outline 1. Introduction Big picture: Want a quantum theory of gravity Best understanding of quantum gravity so far arises through AdS/CFT
More informationThe Generalized Uncertainty Principle and Black Hole Remnants* Ronald J. Adler
The Generalized Uncertainty Principle and Black Hole Remnants* Ronald J. Adler Gravity Probe B, W. W. Hansen Experimental Physics Laboratory Stanford University, Stanford CA 94035 Pisin Chen Stanford Linear
More informationHawking Radiation from Black Holes of Constant Negative Curvature via Gravitational Anomalies
Hawking Radiation from Black Holes of Constant Negative Curvature via Gravitational Anomalies Petros Skamagoulis work with E. Papantonopoulos Phys. Rev. D 79, 0840 (009) [arxiv:081.1759 [hep-th]] Department
More informationAn introduction to General Relativity and the positive mass theorem
An introduction to General Relativity and the positive mass theorem National Center for Theoretical Sciences, Mathematics Division March 2 nd, 2007 Wen-ling Huang Department of Mathematics University of
More informationBlack hole thermodynamics and spacetime symmetry breaking
Black hole thermodynamics and spacetime symmetry breaking David Mattingly University of New Hampshire Experimental Search for Quantum Gravity, SISSA, September 2014 What do we search for? What does the
More informationarxiv:gr-qc/ v1 2 Apr 2002
ENERGY AND MOMENTUM OF A STATIONARY BEAM OF LIGHT Thomas Bringley arxiv:gr-qc/0204006v1 2 Apr 2002 Physics and Mathematics Departments, Duke University Physics Bldg., Science Dr., Box 90305 Durham, NC
More informationChemical Potential in the First Law for Holographic Entanglement Entropy
University of Massachusetts Amherst From the SelectedWorks of David Kastor November 21, 2014 Chemical Potential in the First Law for Holographic Entanglement Entropy David Kastor, University of Massachusetts
More informationPlenty of Nothing: Black Hole Entropy in Induced Gravity
J. Astrophys. Astr. (1999) 20, 121 129 Plenty of Nothing: Black Hole Entropy in Induced Gravity V. P. Frolov, Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, Canada
More informationarxiv:hep-th/ v2 24 Sep 1998
Nut Charge, Anti-de Sitter Space and Entropy S.W. Hawking, C.J. Hunter and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom
More informationProof of the Weak Gravity Conjecture from Black Hole Entropy
Proof of the Weak Gravity Conjecture from Black Hole Entropy Grant N. Remmen Berkeley Center for Theoretical Physics Miller Institute for Basic Research in Science University of California, Berkeley arxiv:1801.08546
More informationHolographic entanglement entropy
Holographic entanglement entropy Mohsen Alishahiha School of physics, Institute for Research in Fundamental Sciences (IPM) 21th Spring Physics Conference, 1393 1 Plan of the talk Entanglement entropy Holography
More informationFinite entropy of Schwarzschild anti-de Sitter black hole in different coordinates
Vol 16 No 12, December 2007 c 2007 Chin. Phys. Soc. 1009-196/2007/16(12/610-06 Chinese Physics and IOP Publishing Ltd Finite entropy of Schwarzschild anti-de Sitter black hole in different coordinates
More informationGravity - Balls. Daksh Lohiya. Inter University Centre for Astromony and Astrophysics. Poona, INDIA. Abstract
Gravity - Balls Daksh Lohiya Inter University Centre for Astromony and Astrophysics [IUCAA], Postbag 4, Ganeshkhind Poona, INDIA Abstract The existence of non trivial, non topological solutions in a class
More informationGeometric Entropy: Black Hole Background
Geometric Entropy: Black Hole Background Frank Wilczek Center for Theoretical Physics, MIT, Cambridge MA 02139 USA March 13, 2014 Abstract I review the derivation of Hawking temperature and entropy through
More informationQuantum Fields in Curved Spacetime
Quantum Fields in Curved Spacetime Lecture 3 Finn Larsen Michigan Center for Theoretical Physics Yerevan, August 22, 2016. Recap AdS 3 is an instructive application of quantum fields in curved space. The
More informationUnruh effect and Holography
nd Mini Workshop on String Theory @ KEK Unruh effect and Holography Shoichi Kawamoto (National Taiwan Normal University) with Feng-Li Lin(NTNU), Takayuki Hirayama(NCTS) and Pei-Wen Kao (Keio, Dept. of
More informationBlack holes and the renormalisation group 1
Black holes and the renormalisation group 1 Kevin Falls, University of Sussex September 16, 2010 1 based on KF, D. F. Litim and A. Raghuraman, arxiv:1002.0260 [hep-th] also KF, D. F. Litim; KF, G. Hiller,
More informationarxiv:gr-qc/ v1 7 Sep 1998
Thermodynamics of toroidal black holes Claudia S. Peça Departamento de Física, Instituto Superior Técnico, Av. Rovisco Pais, 096 Lisboa Codex, Portugal José P. S. Lemos Departamento de Astrofísica. Observatório
More informationarxiv: v1 [gr-qc] 19 Jun 2009
SURFACE DENSITIES IN GENERAL RELATIVITY arxiv:0906.3690v1 [gr-qc] 19 Jun 2009 L. FERNÁNDEZ-JAMBRINA and F. J. CHINEA Departamento de Física Teórica II, Facultad de Ciencias Físicas Ciudad Universitaria,
More informationBest Approximation to a Reversible Process in Black-Hole. Physics and the Area Spectrum of Spherical Black Holes. Abstract
Best Approximation to a Reversible Process in Black-Hole Physics and the Area Spectrum of Spherical Black Holes Shahar Hod The Racah Institute for Physics, The Hebrew University, Jerusalem 91904, Israel
More informationarxiv: v1 [physics.gen-ph] 15 Feb 2011
arxiv:2.395v [physics.gen-ph] 5 Feb 2 Black Hole evaporation in semi-classical approach Shintaro Sawayama Sawayama Cram School of Physics Atsuhara 328, Fuji-shi, Shizuoka-ken, Japan, 49-2 November 2, 28
More informationarxiv: v2 [gr-qc] 28 Dec 2007
IT/CTP-3925 arxiv:0712.3775v2 [gr-qc] 28 Dec 2007 Liouville gravity from Einstein gravity 1 D. Grumiller and R. Jackiw Center for Theoretical Physics, assachusetts Institute of Technology, 77 assachusetts
More informationBLACK HOLES (ADVANCED GENERAL RELATIV- ITY)
Imperial College London MSc EXAMINATION May 2015 BLACK HOLES (ADVANCED GENERAL RELATIV- ITY) For MSc students, including QFFF students Wednesday, 13th May 2015: 14:00 17:00 Answer Question 1 (40%) and
More informationQuantum gravity and entanglement
Quantum gravity and entanglement Ashoke Sen Harish-Chandra Research Institute, Allahabad, India HRI, February 2011 PLAN 1. Entanglement in quantum gravity 2. Entanglement from quantum gravity I shall use
More informationThermodynamics of Schwarzschild-like black holes in bumblebee gravity models. Abstract
Thermodynamics of Schwarzschild-like black holes in bumblebee gravity models D. A. Gomes, R. V. Maluf, and C. A. S. Almeida Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici,
More informationQuark-gluon plasma from AdS/CFT Correspondence
Quark-gluon plasma from AdS/CFT Correspondence Yi-Ming Zhong Graduate Seminar Department of physics and Astronomy SUNY Stony Brook November 1st, 2010 Yi-Ming Zhong (SUNY Stony Brook) QGP from AdS/CFT Correspondence
More informationOn Hidden Symmetries of d > 4 NHEK-N-AdS Geometry
Commun. Theor. Phys. 63 205) 3 35 Vol. 63 No. January 205 On Hidden ymmetries of d > 4 NHEK-N-Ad Geometry U Jie ) and YUE Rui-Hong ) Faculty of cience Ningbo University Ningbo 352 China Received eptember
More informationarxiv: v2 [gr-qc] 21 Oct 2011
hermodynamics of phase transition in higher dimensional AdS black holes Rabin Banerjee, Dibakar Roychowdhury S. N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata-700098,
More information